Properties

Label 116886.c
Number of curves $6$
Conductor $116886$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("116886.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116886.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
116886.c1 116886b6 [1, 1, 0, -9575216, 11400258324] [2] 5242880  
116886.c2 116886b4 [1, 1, 0, -2143396, -1208679776] [2] 2621440  
116886.c3 116886b3 [1, 1, 0, -613956, 168215040] [2, 2] 2621440  
116886.c4 116886b2 [1, 1, 0, -139636, -17244080] [2, 2] 1310720  
116886.c5 116886b1 [1, 1, 0, 15244, -1477296] [2] 655360 \(\Gamma_0(N)\)-optimal
116886.c6 116886b5 [1, 1, 0, 758184, 815041836] [2] 5242880  

Rank

sage: E.rank()
 

The elliptic curves in class 116886.c have rank \(0\).

Modular form 116886.2.a.c

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} - 2q^{5} + q^{6} - q^{7} - q^{8} + q^{9} + 2q^{10} - q^{12} + 2q^{13} + q^{14} + 2q^{15} + q^{16} + 6q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.